# COMBINANDO AS TÉCNICAS DE BUSCA LINEAR COM CONTINUAÇÃO PARA A SOLUÇÃO DE PROBLEMAS ESTRUTURAIS NÃO LINEARES

## Palavras-chave:

nonlinear structural analysis, line search, finite element method## Resumo

The demand for computational tools that simulate the real behavior of structures has been

intensified. Such numerical simulations usually involve highly nonlinear problems. For nonlinear

static problems, in particular, it is fundamental the implementation and use of numerical strategies to

trace the structure equilibrium paths in a complete way, overcoming critical points (limit and

bifurcations points). In the Finite Element Method (FEM) context, where incremental-iterative

strategies are usually adopted, the nonlinear solvers must have a high level of efficiency in the two

phases of the solution process (predictor and corrector), for each load step. In solving the nonlinear

algebraic equations, it is quite common that Newton-Raphson's iterations do not converge or require

an excessive number of iterations near the critical points. Therefore, the linear search optimization

technique appears as an additional sophistication. Basically, this technique aims to stagger the

corrective displacements vector in the iterative phase, seeking to guarantee and accelerate the

convergence of the process. The purpose of this work is to verify the efficiency of linear search

technique coupled with Newton-Raphson iterations and different path-following methods, and verify

its influence on the nonlinear solver efficiency. The effectiveness of the linear search algorithm

implemented is verified in solving slender structures with accentuated nonlinearity. It is previously

perceived that such a resource is triggered near load limit points (with more success when applied to

structures with these critical points), accelerates the iterative process and increases the chances of

convergence.